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25,900 | In statistics, the order of a kernel is the degree of the first non-zero moment of a kernel. | Order of a kernel | 0.807402 |
25,901 | A cognitive computer is a computer that hardwires artificial intelligence and machine-learning algorithms into an integrated circuit (printed circuit board) that closely reproduces the behavior of the human brain. It generally adopts a neuromorphic engineering approach. Synonyms are neuromorphic chip and cognitive chip... | Cognitive computer | 0.807402 |
25,902 | A group with a length function does not form a filtered group, meaning that the sublevel sets S i := { g ∣ L ( g ) ≤ i } {\displaystyle S_{i}:=\{g\mid L(g)\leq i\}} do not form subgroups in general. However, the group algebra of a group with a length functions forms a filtered algebra: the axiom L ( g h ) ≤ L ( g ) + L... | Length function | 0.807402 |
25,903 | A length function L: G → R+ on a group G is a function satisfying: L ( e ) = 0 , L ( g − 1 ) = L ( g ) L ( g 1 g 2 ) ≤ L ( g 1 ) + L ( g 2 ) , ∀ g 1 , g 2 ∈ G . {\displaystyle {\begin{aligned}L(e)&=0,\\L(g^{-1})&=L(g)\\L(g_{1}g_{2})&\leq L(g_{1})+L(g_{2}),\quad \forall g_{1},g_{2}\in G.\end{aligned}}} Compare with the ... | Length function | 0.807402 |
25,904 | The first International Congress on Mathematical Education (ICME) was held in Lyon in 1969. The second congress was in Exeter in 1972, and after that, it has been held every four years.In the 20th century, the cultural impact of the "electronic age" (McLuhan) was also taken up by educational theory and the teaching of ... | Philosophy of mathematics education | 0.807401 |
25,905 | Consider a monoid M. Consider a pair (A,L) where A is a finite subset of M that generates M as a monoid, and L is a language on A (that is, a subset of the set of all strings A∗). Let φ be the map from the free monoid A∗ to M given by evaluating a string as a product in M. We say that L is a rational cross-section if φ... | Rational monoid | 0.807401 |
25,906 | Kleene's theorem holds for rational monoids: that is, a subset is a recognisable set if and only if it is a rational set. A rational monoid is not necessarily automatic, and vice versa. However, a rational monoid is asynchronously automatic and hyperbolic. A rational monoid is a regulator monoid and a quasi-rational mo... | Rational monoid | 0.807401 |
25,907 | Suffix trees are powerful data structures that have wide application in areas of pattern and string matching, indexing and textual statistics. However, it occupies a significant amount of space and thus has a drawback in many real-time applications that require processing a considerably large amount of data like genome... | Suffix array | 0.807401 |
25,908 | In computer science, a suffix array is a sorted array of all suffixes of a string. It is a data structure used in, among others, full-text indices, data-compression algorithms, and the field of bibliometrics. Suffix arrays were introduced by Manber & Myers (1990) as a simple, space efficient alternative to suffix trees... | Suffix array | 0.807401 |
25,909 | Therapeutic drug monitoring (TDM) is a branch of clinical chemistry and clinical pharmacology that specializes in the measurement of medication levels in blood. Its main focus is on drugs with a narrow therapeutic range, i.e. drugs that can easily be under- or overdosed. TDM aimed at improving patient care by individua... | Therapeutic drug monitoring | 0.8074 |
25,910 | A priori TDM consists of determining the initial dose regimen to be given to a patient, based on clinical endpoint and on established population pharmacokinetic-pharmacodynamic (PK/PD) relationships. These relationships help to identify sub-populations of patients with different dosage requirements, by utilizing demogr... | Therapeutic drug monitoring | 0.8074 |
25,911 | In pharmacotherapy, many medications are used without monitoring of blood levels, as their dosage can generally be varied according to the clinical response that a patient gets to that substance. For certain drugs, this is impracticable, while insufficient levels will lead to undertreatment or resistance, and excessive... | Therapeutic drug monitoring | 0.8074 |
25,912 | They collect population data, the first step to allowing for policy making on disease control, nations must first collect data on air travel as billions of people travel by air each year and sea travel. Air travel carries more people each year than sea shipments, but the primary reason for collecting data on shipments ... | Reality mining | 0.807397 |
25,913 | This new way of understanding data opened up doors for new research and possibly even larger survey research with detailed and accurate statistics. There are hundreds of websites offering software for mobile phones that will track just about everything the phone does, useful for worried parents or people who want to in... | Reality mining | 0.807397 |
25,914 | The actual amount of disk space consumed by the file depends on the file system. The maximum file size a file system supports depends on the number of bits reserved to store size information and the total size of the file system in terms of its capacity to store bits of information. In physics, the Planck length, denot... | Physical dimension | 0.807393 |
25,915 | There are various other mathematical concepts of size for sets, such as: measure (mathematics), a systematic way to assign to each suitable subset a number cardinality (equal if there is a bijection), of a set is a measure of the "number of elements of the set" for well-ordered sets: ordinal number (equal if there is a... | Physical dimension | 0.807393 |
25,916 | Sender and receiver can generate the same set of numbers automatically to use as keys. The generation of pseudorandom numbers is an important and common task in computer programming. While cryptography and certain numerical algorithms require a very high degree of apparent randomness, many other operations only need a ... | Random generator | 0.807392 |
25,917 | Random number generators have applications in gambling, statistical sampling, computer simulation, cryptography, completely randomized design, and other areas where producing an unpredictable result is desirable. Generally, in applications having unpredictability as the paramount feature, such as in security applicatio... | Random generator | 0.807392 |
25,918 | The GM406 has a transmitter which is twice as powerful as the GM403, giving it 20% greater range, increasing from 390 km to 450 km. The GM406 is primarily designed to equip fixed sites, with the GM403 designed to be deployable. In 2021, Thales introduced a new version, GM400α, with 5 times more processing power, extend... | Ground Master 400 | 0.807392 |
25,919 | Retrospective studies have disadvantages vis-a-vis prospective studies: Some key statistics cannot be measured, and significant biases may affect the selection of controls. Researchers cannot control exposure or outcome assessment, and instead must rely on others for accurate recordkeeping. When relying on individual r... | Retrospective cohort study | 0.807391 |
25,920 | Lagrange multipliers: constrained critical points are where the tangential component of the total derivative vanish. Surface normal Frenet–Serret formulas Differential geometry of surfaces § Tangent vectors and normal vectors | Tangential and normal components | 0.80739 |
25,921 | Some Europeans maintained the Aristotelian view that infinity could only be seen as an attribute of God, with the cosmos being finite. Furthermore, following the Aristotelian view that "nature abhors a vacuum", some Europeans believed that the space between the spheres were filled with air. This theory persisted until ... | Cosmos | 0.80739 |
25,922 | Commonly regarded as the foundation of modern astronomy, the common universal view of the cosmos shifted as Nicolaus Copernicus positioned the Sun as the center of the Universe. | Cosmos | 0.80739 |
25,923 | Australian cosmology has a vast and varied history.Australian cosmology beliefs were based around the Aboriginal and Torres Strait Islander people's ideas, also known as Indigenous astronomy, and it was around before the Babylonians, Greeks, and the Renaissance period. They found ways to observe the Moon, stars, and th... | Cosmos | 0.80739 |
25,924 | Astronomer and mathematician Nicolaus Copernicus was appointed by the Catholic Church as an official, as his uncle was a bishop in the church. He used his income to further his studies, eventually studying at the University of Bologna in Italy. Copernicus began doubting the knowledge of natural philosophers and their b... | Cosmos | 0.80739 |
25,925 | Anaximander was a pre-Socratic Greek philosopher who is widely referred to as the "father of astronomy" and even as the "father of cosmology" as a result of his works to explain the origin and makeup of the physical universe. He is regarded as the most important of the Ionian philosophers, and was a pupil of Thales. Tr... | Cosmos | 0.80739 |
25,926 | Physical cosmology has achieved a consensus Standard Model (SM), based on extending the local physics governing gravity and the other forces to describe the overall structure of the universe and its evolution. According to the SM, the universe has evolved from an extremely high temperature early state, by expanding, co... | Cosmos | 0.80739 |
25,927 | Cosmology is a branch of metaphysics that deals with the nature of the universe, a theory or doctrine describing the natural order of the universe. The basic definition of Cosmology is the science of the origin and development of the universe. In modern astronomy, the Big Bang theory is the dominant postulation. Philos... | Cosmos | 0.80739 |
25,928 | Random number generators are important in many kinds of technical applications, including physics, engineering or mathematical computer studies (e.g., Monte Carlo simulations), cryptography and gambling (on game servers). This list includes many common types, regardless of quality or applicability to a given use case. | List of random number generators | 0.80739 |
25,929 | Freeze fracture enzyme cytochemistry was initially mentioned in the study of Pinto de silva in 1987. It is a technique that allows the introduction of cytochemistry into a freeze fracture cell membrane. immunocytochemistry is used in this technique to label and visualize the cell membrane's molecules. This technique co... | Cytochemistry | 0.807389 |
25,930 | Jean Brachet's research in Brussel demonstrated the localization and relative abundance between RNA and DNA in the cells of both animals and plants opened up the door into the research of cytochemistry. The work by Moller and Holter in 1976 about endocytosis which discussed the relationship between a cell's structure a... | Cytochemistry | 0.807389 |
25,931 | Cytochemistry is the branch of cell biology dealing with the detection of cell constituents by means of biochemical analysis and visualization techniques. This is the study of the localization of cellular components through the use of staining methods. The term is also used to describe a process of identification of th... | Cytochemistry | 0.807389 |
25,932 | Analogously, nonlinearity or forcing in the system perturbs the stable and unstable eigenspaces to a nearby stable manifold and nearby unstable manifold. These three types of manifolds are three cases of an invariant manifold. Algebraically, let d x d t = f ( x ) {\displaystyle {\frac {d{\textbf {x}}}{dt}}={\textbf {f}... | Center manifold | 0.807388 |
25,933 | The (generalized) eigenvectors corresponding to eigenvalues with positive real part form the unstable eigenspace. If the equilibrium point is hyperbolic (that is, all eigenvalues of the linearization have nonzero real part), then the Hartman-Grobman theorem guarantees that these eigenvalues and eigenvectors completely ... | Center manifold | 0.807388 |
25,934 | However, some applications, such as to dispersion in tubes or channels, require an infinite-dimensional center manifold. The most general and powerful theory was developed by Aulbach and Wanner. They addressed non-autonomous dynamical systems d x d t = f ( x , t ) {\displaystyle {\frac {d{\textbf {x}}}{dt}}={\textbf {f... | Center manifold | 0.807388 |
25,935 | As the stability of the equilibrium correlates with the "stability" of its manifolds, the existence of a center manifold brings up the question about the dynamics on the center manifold. This is analyzed by the center manifold reduction, which, in combination with some system parameter μ, leads to the concepts of bifur... | Center manifold | 0.807388 |
25,936 | Mandala Vaatikas or Sacred Gardens were designed using the same principles. Many of the sacred geometry principles of the human body and of ancient architecture were compiled into the Vitruvian Man drawing by Leonardo da Vinci. The latter drawing was itself based on the much older writings of the Roman architect Vitruv... | Sacred Geometry | 0.807386 |
25,937 | Geometric ratios, and geometric figures were often employed in the designs of ancient Egyptian, ancient Indian, Greek and Roman architecture. Medieval European cathedrals also incorporated symbolic geometry. Indian and Himalayan spiritual communities often constructed temples and fortifications on design plans of manda... | Sacred Geometry | 0.807386 |
25,938 | The repetition of these replication parts symbolizes the natural phenomena of fractal patterns found in nature. These patterns make up the exterior of Hindu temples. Each element and detail are proportional to each other, this occurrence is also known as the sacred geometry. | Sacred Geometry | 0.807386 |
25,939 | Stephen Skinner criticizes the tendency of some writers to place a geometric diagram over virtually any image of a natural object or human created structure, find some lines intersecting the image and declare it based on sacred geometry. If the geometric diagram does not intersect major physical points in the image, th... | Sacred Geometry | 0.807386 |
25,940 | Sacred geometry ascribes symbolic and sacred meanings to certain geometric shapes and certain geometric proportions. It is associated with the belief of a divine creator of the universal geometer. The geometry used in the design and construction of religious structures such as churches, temples, mosques, religious monu... | Sacred Geometry | 0.807386 |
25,941 | Harvard mathematician Shing-Tung Yau expressed a belief in the centrality of geometry in 2010: "Lest one conclude that geometry is little more than a well-calibrated ruler – and this is no knock against the ruler, which happens to be a technology I admire – geometry is one of the main avenues available to us for probin... | Sacred Geometry | 0.807386 |
25,942 | According to Stephen Skinner, the study of sacred geometry has its roots in the study of nature, and the mathematical principles at work therein. Many forms observed in nature can be related to geometry; for example, the chambered nautilus grows at a constant rate and so its shell forms a logarithmic spiral to accommod... | Sacred Geometry | 0.807386 |
25,943 | The construction of Medieval European cathedrals was often based on geometries intended to make the viewer see the world through mathematics, and through this understanding, gain a better understanding of the divine. These churches frequently featured a Latin Cross floor-plan.At the beginning of the Renaissance in Euro... | Sacred Geometry | 0.807386 |
25,944 | Room layout is also an important element, as doors should be proportional to one another and located at appropriate positions throughout the house. Typically, doors are not situated across from one another because it may cause Chi to flow too fast from one room to the next.The Forbidden City is an example of a building... | Sacred Geometry | 0.807386 |
25,945 | For example, there exists an analog of the celebrated Serre duality for noncommutative projective schemes of Artin and Zhang.A. L. Rosenberg has created a rather general relative concept of noncommutative quasicompact scheme (over a base category), abstracting Grothendieck's study of morphisms of schemes and covers in ... | Non-commutative geometry | 0.807385 |
25,946 | This theorem is extended as a definition of noncommutative projective geometry by Michael Artin and J. J. Zhang, who add also some general ring-theoretic conditions (e.g. Artin–Schelter regularity). Many properties of projective schemes extend to this context. | Non-commutative geometry | 0.807385 |
25,947 | In analogy to the duality between affine schemes and commutative rings, we define a category of noncommutative affine schemes as the dual of the category of associative unital rings. There are certain analogues of Zariski topology in that context so that one can glue such affine schemes to more general objects. There a... | Non-commutative geometry | 0.807385 |
25,948 | A Connes connection is a noncommutative generalization of a connection in differential geometry. It was introduced by Alain Connes, and was later generalized by Joachim Cuntz and Daniel Quillen. | Non-commutative geometry | 0.807385 |
25,949 | The Marcus equation is an example of a quadratic free-energy relationship (QFER). IUPAC has suggested that this name should be replaced by linear Gibbs energy relation, but at present there is little sign of acceptance of this change. The area of physical organic chemistry which deals with such relations is commonly re... | Linear free energy relationship | 0.807382 |
25,950 | In physical organic chemistry, a free-energy relationship or Gibbs energy relation relates the logarithm of a reaction rate constant or equilibrium constant for one series of chemical reactions with the logarithm of the rate or equilibrium constant for a related series of reactions. Free energy relationships establish ... | Linear free energy relationship | 0.807382 |
25,951 | : 383 Harel also writes that the more generic name was proposed by H.D. Mills as "The Structure Theorem" in the early 1970s. : 381 | Structured program theorem | 0.807382 |
25,952 | The theorem is typically credited: 381 to a 1966 paper by Corrado Böhm and Giuseppe Jacopini. David Harel wrote in 1980 that the Böhm–Jacopini paper enjoyed "universal popularity",: 381 particularly with proponents of structured programming. Harel also noted that "due to its rather technical style is apparently more o... | Structured program theorem | 0.807382 |
25,953 | The structured program theorem, also called the Böhm–Jacopini theorem, is a result in programming language theory. It states that a class of control-flow graphs (historically called flowcharts in this context) can compute any computable function if it combines subprograms in only three specific ways (control structures... | Structured program theorem | 0.807382 |
25,954 | McCabe also devised a numerical measure that, given an arbitrary program, quantifies how far off it is from the ideal of being a structured program; McCabe called his measure essential complexity.McCabe's characterization of the forbidden graphs for structured programming can be considered incomplete, at least if the D... | Structured program theorem | 0.807382 |
25,955 | (This is a narrower notion of reducibility than what Böhm–Jacopini used.) Inspired by this result, in section VI of his highly-cited paper that introduced the notion of cyclomatic complexity, Thomas J. McCabe described an analogue of Kuratowski's theorem for the control-flow graphs (CFG) of non-structured programs, whi... | Structured program theorem | 0.807382 |
25,956 | The pragmatic counterpoint was that such transformations benefited a large body of existing programs. Among the first proposals for an automated transformation was a 1971 paper by Edward Ashcroft and Zohar Manna.The direct application of the Böhm–Jacopini theorem may result in additional local variables being introduce... | Structured program theorem | 0.807382 |
25,957 | : 383 Another, even older source that Harel traced the folk version of the theorem is Stephen Kleene's normal form theorem from 1936.: 383 Donald Knuth criticized this form of the proof, which results in pseudocode like the one below, by pointing out that the structure of the original program is completely lost in this... | Structured program theorem | 0.807382 |
25,958 | This version of the theorem replaces all the original program's control flow with a single global while loop that simulates a program counter going over all possible labels (flowchart boxes) in the original non-structured program. Harel traced the origin of this folk theorem to two papers marking the beginning of compu... | Structured program theorem | 0.807382 |
25,959 | Critics of this approach complain that it is too slow for real-time planning and that, despite the proofs, it is still unlikely to produce optimal plans because reducing descriptions of reality to logic is a process prone to errors. Satisficing is a decision-making strategy that attempts to meet criteria for adequacy, ... | Action selection | 0.807381 |
25,960 | Early in the history of artificial intelligence, it was assumed that the best way for an agent to choose what to do next would be to compute a probably optimal plan, and then execute that plan. This led to the physical symbol system hypothesis, that a physical agent that can manipulate symbols is necessary and sufficie... | Action selection | 0.807381 |
25,961 | Excalibur was a research project led by Alexander Nareyek featuring any-time planning agents for computer games. The architecture is based on structural constraint satisfaction, which is an advanced artificial intelligence technique. | Action selection | 0.807381 |
25,962 | The action selection mechanism (ASM) determines not only the agent's actions in terms of impact on the world, but also directs its perceptual attention, and updates its memory. These egocentric sorts of actions may in turn result in modifying the agent's basic behavioural capacities, particularly in that updating memor... | Action selection | 0.807381 |
25,963 | For biology and ethology, the question is how do various types of animals constrain their search? Do all animals use the same approaches? Why do they use the ones they do? | Action selection | 0.807381 |
25,964 | Action selection is a way of characterizing the most basic problem of intelligent systems: what to do next. In artificial intelligence and computational cognitive science, "the action selection problem" is typically associated with intelligent agents and animats—artificial systems that exhibit complex behaviour in an a... | Action selection | 0.807381 |
25,965 | Some researchers create elaborate models of neural action selection. See for example: The Computational Cognitive Neuroscience Lab (CU Boulder). The Adaptive Behaviour Research Group (Sheffield). | Action selection | 0.807381 |
25,966 | In recent years, plant physiologists have examined the physiology of plant behavior and cognition. The concepts of learning and memory are relevant in identifying how plants respond to external cues, a behavior necessary for survival. Monica Gagliano, an Australian professor of evolutionary ecology, makes an argument f... | Non-associative learning | 0.80738 |
25,967 | With the growing interest and technological developments in quantum computing, IEEE determined in 2018 to expand its role in establishing metrics and benchmarks in this nascent field. This effort has been led by Dr. Erik DeBenedictis, one of the co-chairs of Rebooting Computing. An invitation-only Summit was held in Au... | IEEE Rebooting Computing | 0.807379 |
25,968 | With the goal of identifying new directions in computing and aiding industry in returning to historical exponential scaling of computer performance, IEEE Rebooting Computing encompasses a variety of activities, products, and services. Among these efforts are an online web portal, technical community, publications, conf... | IEEE Rebooting Computing | 0.807379 |
25,969 | In October 2017, a three-day IEEE Confluence Event was held, bringing together leaders in the fields of cybersecurity and artificial intelligence/machine learning (AI/ML). This workshop was co-chaired by Dr. Dejan Milojicic, co-chair of Rebooting Computing. The aim was to develop a strategy to coordinate efforts to app... | IEEE Rebooting Computing | 0.807379 |
25,970 | A third LPIRC was held in July 2017 as part of the Computer Vision and Pattern Recognition Conference (CVPR) in Honolulu, Hawaii. In 2018, two LPIRC competitions were held, one at CVPR in Salt Lake City, Utah in June, and a second online competition in November. These included major new sponsors Google and Facebook. LP... | IEEE Rebooting Computing | 0.807379 |
25,971 | government, announced a "Nanotechnology-Inspired Grand Challenge in Future Computing". A key document cited by NNI as part of this grand challenge is a white paper, co-sponsored by IEEE Rebooting Computing and ITRS, entitled Sensible Machines.In 2017, the IEEE New Initiatives Committee renewed the mandate of the Reboot... | IEEE Rebooting Computing | 0.807379 |
25,972 | In September 2015, IEEE Rebooting Computing announced support for the National Strategic Computing Initiative (NSCI). Established under Executive Order 13072 issued by U.S. President Barack Obama in July 2015, the NSCI calls for a coordinated Federal strategy in high-performance computing (HPC) research, development, a... | IEEE Rebooting Computing | 0.807379 |
25,973 | A larger, open conference, the IEEE International Conference on Rebooting Computing (ICRC 2016), was held in October 2016, in San Diego, California. The goal of ICRC 2016 was to discover and foster novel methodologies to reinvent computing technology, including new materials and physics, devices and circuits, system an... | IEEE Rebooting Computing | 0.807379 |
25,974 | Starting in 2017, “Rebooting Computing Week” was created to have a common location for annual conferences and workshops associated with Rebooting Computing. In 2017 and 2018, this was held in November in the Washington, DC area. Events in 2018 included ICRC, the Industry Summit, IRDS Workshop, the Cybersecurity Worksho... | IEEE Rebooting Computing | 0.807379 |
25,975 | In November 2017, IEEE Rebooting Computing also sponsored a distinct one-day summit, following ICRC, which addressed similar topics but with a somewhat different focus and audience. This Industry Summit featured plenary presentations by industry, government, and academic leaders on what we can expect for new computer t... | IEEE Rebooting Computing | 0.807379 |
25,976 | IEEE Rebooting Computing began as a multi-society participation from a cross-section of IEEE societies with interest in numerous aspects of computing, including circuits and systems design; architectures; design automation; magnetics; nanotechnology; reliability; and superconductors.IEEE Societies and Councils taking p... | IEEE Rebooting Computing | 0.807379 |
25,977 | Goal misgeneralization has been observed in language models, navigation agents, and game-playing agents.Goal misgeneralization is often explained by analogy to biological evolution. : Chapter 5 Evolution is an optimization process of a sort, like the optimization algorithms used to train machine learning systems. In th... | AI alignment | 0.807379 |
25,978 | One of the challenges with aligning AI systems is the potential for unanticipated goal-directed behavior to emerge. As AI systems scale up they regularly acquire new and unexpected capabilities, including learning from examples on the fly and adaptively pursuing goals. This leads to the problem of ensuring that the goa... | AI alignment | 0.807379 |
25,979 | The strategy describes actions to assess long term AI risks, including catastrophic risks.In March 2021, the US National Security Commission on Artificial Intelligence stated that "Advances in AI... could lead to inflection points or leaps in capabilities. Such advances may also introduce new concerns and risks and the... | AI alignment | 0.807379 |
25,980 | In honour of the many contributions of John Selfridge to mathematics, the Number Theory Foundation has established a prize to be awarded to those individuals who have authored the best paper accepted for presentation at ANTS. The prize, called the Selfridge Prize, is awarded every two years in an even numbered year. Th... | Algorithmic Number Theory Symposium | 0.807377 |
25,981 | Prior to ANTS X, the refereed Proceedings of ANTS were published in the Springer Lecture Notes in Computer Science (LNCS). The proceedings of ANTS X, ANTS XIII, and ANTS XIV were published in the Mathematical Sciences Publishers Open Book Series (OBS). The proceedings of ANTS XI and ANTS XII were published as a special... | Algorithmic Number Theory Symposium | 0.807377 |
25,982 | Algorithmic Number Theory Symposium (ANTS) is a biennial academic conference, first held in Cornell in 1994, constituting an international forum for the presentation of new research in computational number theory. They are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic nu... | Algorithmic Number Theory Symposium | 0.807377 |
25,983 | The IJCAI Computers and Thought Award is presented every two years by the International Joint Conference on Artificial Intelligence (IJCAI), recognizing outstanding young scientists in artificial intelligence. It was originally funded with royalties received from the book Computers and Thought (edited by Edward Feigenb... | IJCAI Computers and Thought Award | 0.807375 |
25,984 | Terry Winograd (1971) Patrick Winston (1973) Chuck Rieger (1975) Douglas Lenat (1977) David Marr (1979) Gerald Sussman (1981) Tom Mitchell (1983) Hector Levesque (1985) Johan de Kleer (1987) Henry Kautz (1989) Rodney Brooks (1991) Martha E. Pollack (1991) Hiroaki Kitano (1993) Sarit Kraus (1995) Stuart Russell (1995) L... | IJCAI Computers and Thought Award | 0.807375 |
25,985 | In organometallic chemistry, a transition metal alkyne complex is a coordination compound containing one or more alkyne ligands. Such compounds are intermediates in many catalytic reactions that convert alkynes to other organic products, e.g. hydrogenation and trimerization. | Alkyne complex | 0.807371 |
25,986 | Typically, gradient descent is preferred, even if requires a large number of iterations, because, it can be hard to compute the second-order derivative (that is, the Hessian) of the objective functional F {\displaystyle {\mathcal {F}}} . If the shape optimization problem has constraints, that is, the functional G {\dis... | Shape optimization | 0.807369 |
25,987 | Shape optimization problems are usually solved numerically, by using iterative methods. That is, one starts with an initial guess for a shape, and then gradually evolves it, until it morphs into the optimal shape. | Shape optimization | 0.807369 |
25,988 | For A ∈ C m × n {\displaystyle A\in \mathbb {C} ^{m\times n}} , and i = 1 , 2 , … , min { m , n } {\displaystyle i=1,2,\ldots ,\min\{m,n\}} . Min-max theorem for singular values. Here U: dim ( U ) = i {\displaystyle U:\dim(U)=i} is a subspace of C n {\displaystyle \mathbb {C} ^{n}} of dimension i {\displaystyle i} . ... | Singular values | 0.807369 |
25,989 | The singular values are the absolute values of the eigenvalues of a normal matrix A, because the spectral theorem can be applied to obtain unitary diagonalization of A {\displaystyle A} as A = U Λ U ∗ {\displaystyle A=U\Lambda U^{*}} . Therefore, A ∗ A = U Λ ∗ Λ U ∗ = U | Λ | U ∗ {\textstyle {\sqrt {A^{*}A}}={\sqrt {U\... | Singular values | 0.807369 |
25,990 | In mathematics, in particular functional analysis, the singular values, or s-numbers of a compact operator T: X → Y {\displaystyle T:X\rightarrow Y} acting between Hilbert spaces X {\displaystyle X} and Y {\displaystyle Y} , are the square roots of the (necessarily non-negative) eigenvalues of the self-adjoint operator... | Singular values | 0.807369 |
25,991 | In graph theory, a branch of mathematics, a split graph is a graph in which the vertices can be partitioned into a clique and an independent set. Split graphs were first studied by Földes and Hammer (1977a, 1977b), and independently introduced by Tyshkevich and Chernyak (1979).A split graph may have more than one parti... | Split graph | 0.807367 |
25,992 | The double split graphs, a family of graphs derived from split graphs by doubling every vertex (so the clique comes to induce an antimatching and the independent set comes to induce a matching), figure prominently as one of five basic classes of perfect graphs from which all others can be formed in the proof by Chudnov... | Split graph | 0.807367 |
25,993 | In this case, i ∪ {x} is a maximum independent set and C is a maximum clique. C is a maximal clique and i is a maximal independent set. In this case, G has a unique partition (C, i) into a clique and an independent set, C is the maximum clique, and i is the maximum independent set.Some other optimization problems that ... | Split graph | 0.807367 |
25,994 | In organic chemistry, the high dilution principle is a strategy for some macrocyclization reactions, i.e. the synthesis of macrocycles. Unlike the synthesis of 5- and 6-membered rings, the preparation of larger rings competes unfavorably with polymerization reactions. Polymers arise from coupling of long chain precurso... | High dilution principle | 0.807365 |
25,995 | MacArthur and Levins were the first to introduce the term 'limiting similarity' in their 1967 paper. They attempted to lay out a rigorous quantitative basis for the theory using probability theory and the Lotka–Volterra competition equations. In doing so, they provided the ultimate theoretical framework on which many s... | Limiting similarity | 0.807364 |
25,996 | It is of note that the theory of limiting similarity does not easily generate falsifiable predictions about natural phenomenon. However, many studies have tried to test the theory by making the highly suspect assumption that character displacement can be used as a close proxy for niche incongruence. One recent paleoeco... | Limiting similarity | 0.807364 |
25,997 | Limiting similarity (informally "limsim") is a concept in theoretical ecology and community ecology that proposes the existence of a maximum level of niche overlap between two given species that will allow continued coexistence. This concept is a corollary of the competitive exclusion principle, which states that, cont... | Limiting similarity | 0.807364 |
25,998 | Yaroshevsky, Earth's Crust Geochemistry, in Encyclopedia of Geochemistry and Environmental Sciences, R.W. Fairbridge (ed. ), Van Nostrand, New York, (1969). | Abundances of the elements (data page) | 0.807364 |
25,999 | I. Bodek et al., Environmental Inorganic Chemistry, Pergamon Press, New York, (1988). A.B. Ronov, A.A. | Abundances of the elements (data page) | 0.807364 |
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